Abstract

Reconstructing a hologram with spatially incoherent illumination smears the obtained image. We propose a wavelet based holographic recording process which uses the smearing to obtain a reconstruction with improved spatial resolution when incoherent illumination is applied.

© 2002 Optical Society of America

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
    [CrossRef] [PubMed]
  2. D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
    [CrossRef]
  3. D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
    [CrossRef]
  4. E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Tech. 41, 201–204 (1997).
  5. W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
    [CrossRef] [PubMed]
  6. A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor-Mikroskop,” Opt. Acta 3, 97–100 (1956).
    [CrossRef]
  7. E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  8. J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).
    [CrossRef]
  9. S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).
  10. R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
    [CrossRef]
  11. Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).
  12. D. J. DeBotteto, “Holographic panoramic stereogram synthesis from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
    [CrossRef]
  13. J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
    [CrossRef]

1997 (1)

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Tech. 41, 201–204 (1997).

1969 (2)

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

D. J. DeBotteto, “Holographic panoramic stereogram synthesis from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
[CrossRef]

1968 (2)

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).
[CrossRef]

1967 (1)

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

1964 (1)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

1962 (1)

1956 (1)

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor-Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

1951 (1)

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

1950 (1)

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Benton, S. A.

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

Bragg, W. L.

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

DeBotteto, D. J.

Denisyuk, Y. N.

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

George, N.

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

Leith, E. N.

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Tech. 41, 201–204 (1997).

E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor-Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

McCrickerd, J. T.

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

Pole, R. V.

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

Redman, J. D.

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).
[CrossRef]

Upatnieks, J.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. T. McCrickerd, N. George, “Holographic stereogram from sequential components photographs,” Appl. Phys. Lett. 12, 10–12 (1968).
[CrossRef]

R. V. Pole, “3-D imaging and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10, 20–22 (1967).
[CrossRef]

J. Imaging Sci. Tech. (1)

E. N. Leith, “Overview of the development of holography,” J. Imaging Sci. Tech. 41, 201–204 (1997).

J. Opt. Soc. Am. (2)

E. N. Leith, J. Upatnieks, “Wavefront reconstruction and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
[CrossRef]

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545–1546 (1969).

J. Sci. Instrum. (1)

J. D. Redman, “Novel approach to holography,” J. Sci. Instrum. 1, 821–822 (1968).
[CrossRef]

Nature (2)

W. L. Bragg, “Microscopy by reconstructed wave fronts,” Nature 166, 399–400 (1950).
[CrossRef] [PubMed]

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Opt. Acta (1)

A. W. Lohmann, “Optische einseitenbandubertragung angewandt auf das Gabor-Mikroskop,” Opt. Acta 3, 97–100 (1956).
[CrossRef]

Opt. Spectrosc. (1)

Y. N. Denisyuk, “On the reproduction of the optical properties of an object by the wave fields of its scattered radiation,” Opt. Spectrosc. 15, 279–284 (1964).

Proc. Phys. Soc. London Sect. B (1)

D. Gabor, “Microscopy by reconstructed wave fronts II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Gabor, “Microscopy by reconstructed wave fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Modeling of incoherent holographic reconstruction.

Fig. 2
Fig. 2

Structure of the wavelet encoding holographic recording.

Fig. 3
Fig. 3

Optical configuration used for the incoherent holographic recording.

Fig. 4
Fig. 4

Incoherent holographic reconstruction of each wavelet harmonic: (a) Hologram of the original slit object 8-mm wide, (b) A hologram of the object scaled to 4-mm wide, (c) 2-mm wide object, (d) 1-mm wide object.

Fig. 5
Fig. 5

Reconstruction of the hologram with coherent illumination for the original object (8-mm wide).

Fig. 6
Fig. 6

Projection of: (a) Fig. 4(a), (b) Fig. 5, (c) Both projections are on top of one another.

Fig. 7
Fig. 7

Obtained results with wavelet encoding: (a) the 2-D image display, (b) the projection of (a).

Equations (21)

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J12x1, x2=u2x1u2*x2 = u1x¯1u1*x¯2×hx1-x¯1h*x2-x¯2dx¯1dx¯2,
u1x¯1u1*x¯2=Iinδx¯1-x¯2J12x1, x2= Iinδx¯1-x¯2hx1-x¯1×h*x2-x¯2dx¯1dx¯2 =Iin  hx1-x¯1h*x2-x¯1dx¯1.
J12x1, x2=Gx1exp2πix1αG*x2×exp-2πix2αJ12x1, x2.
Gμ= gxexp-2πixμdx
I0μ= J12x1, x2exp-2πiμx1×exp2πiμx2dx1dx2,
I0μ=Iin exp2πiz1x¯1Hz1gμ-α-z1×exp-2πiz2x¯1 · H*z2g*μ-α-z2×dx¯1dz1dz2,
Hμ= hxexp-2πixμdx
 exp-2πix1z2-z1dx¯1=δz2-z1,
I0μ= |Hz|2|gμ-α-z|2dz.
Wa, bx, by=1a  fx, yhx-bxa, y-byadxdy,
fx, y=1C  Wa, bx, bya3×hx-bxa, y-byadadbxdby,
fx, y=1Cn  W2n, bx, by23n×hx-bx2n, y-by2ndbxdby.
Wa, bx, by=a  fax+bx, ay+byhx, ydxdy, a=2n,
Wa, b=1a  fxhx-badx,
Wa, b=a  fax+bhxdx a=2n
fx=1Cn  W2n, b22n2n hx-b2ndb.
Gbx, by=nW2n, 2nbx-Δx, 2nby-Δy2n =n f2nx-Δx, 2ny-Δy  hx, y,
fx, y=1C  Gx-bx, y-byhbx, bydbxdby.
fx, y=1CGx, y  hx, y=1Cn f2nx, 2ny  hx, y  hx, y,
Gb=nW2n, 2nb-Δx2n2n=nf2nx-Δx2n  hx,
fx=1C  Gx-bhbdb=1Cnf2nx2n  hx  hx,

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